Airplanes

Airplanes

Many of you have asked yourself how are airplanes able to fly if they are so heavy. The only way to explain this mind blowing fact is physics. An airplane has to be moving at a very high level to be able to fly. Air friction is then created and allows the plane not to fall down. An other factor are the wings. The wings allow the plane to "float" on air. They cut through the air and in a sort of way lay on air. This is also thanks to air friction. Without our atmosphere, not only we would die, we wouldn't be able to fly.

Their are many different types of planes. Each plane require different explanations to state how they work. Physics is once again essentiel to explain to phenomenas. Their are planes that have the capability to land in water. Those plans obviously need different modifications to be able to float. They now have to be light weight and use materials that won't sink. Plans who land on normal grounds have to be equipped with wheels and have to make contact with a fairly low speed to make sure they don't crash.

Planes can also reach speeds faster than the speed of sound. They have engines engineered to fly at speeds that can defy the speed of sound. Those planes are obviously lighter and more aerodynamic.

To conclude, planes require a lot of physics and are based on a lot of physics theories. They might look magical at some times, but they are not.

Rainbows

Rainbow Formation 

Craig Kelleher 

        One of nature's most splendid masterpieces is the rainbow. A rainbow is an excellent demonstration of the dispersion of light and one more piece of evidence that visible light is composed of a spectrum of wavelengths, each associated with a distinct color. To view a rainbow, your back must be to the sun as you look at an approximately 40 degree angle above the ground into a region of the atmosphere with suspended droplets of water or even a light mist. Each individual droplet of water acts as a tiny prism that both disperses the light and reflects it back to your eye. As you sight into the sky, wavelengths of light associated with a specific color arrive at your eye from the collection of droplets. The net effect of the vast array of droplets is that a circular arc is seen across the sky. But just exactly how do the droplets of water disperse and reflect the light? 

      The Path of Light Through a Droplet

        A collection of suspended water droplets in the atmosphere serves as a refractor of light. The water represents a medium with a different optical density than the surrounding air. Light waves refract when they cross over the boundary from one medium to another. The decrease in speed upon entry of light into a water droplet causes a bending of the path of light towards the normal. And upon exiting the droplet, light speeds up and bends away from the normal. The droplet causes a deviation in the path of light as it enters and exits the drop.

        There are countless paths by which light rays from the sun can pass through a drop. Each path is characterized by this bending towards and away from the normal. One path of great significance in the discussion of rainbows is the path in which light refracts into the droplet, internally reflects, and then refracts out of the droplet. The diagram at the right depicts such a path. A light ray from the sun enters the droplet with a slight downward trajectory. Upon refracting twice and reflecting once, the light ray is dispersed and bent downward towards an observer on earth's surface

        The angle of deviation between the incoming light rays from the sun and the refracted rays directed to the observer's eyes is approximately 42 degrees for the red light. Because of the tendency of shorter wavelength blue light to refract more than red light, its angle of deviation from the original sun rays is approximately 40 degrees. As shown in the diagram, the red light refracts out of the droplet at a steeper angle toward an observer on the ground. There are a multitude of paths by which the original ray can pass through a droplet and subsequently angle towards the ground.

How They Form 

        A rainbow is most often viewed as a circular arc in the sky. An observer on the ground observes a half-circle of color with red being the color perceived on the outside or top of the bow. Those who are fortunate enough to have seen a rainbow from an airplane in the sky may know that a rainbow can actually be a complete circle. Observers on the ground only view the top half of the circle since the bottom half of the circular arc is prevented by the presence of the ground (and the rather obvious fact that suspended water droplets aren't present below ground). Yet observers in an airborne plane can often look both upward and downward to view the complete circular bow.

        The circle (or half-circle) results because there are a collection of suspended droplets in the atmosphere that are capable concentrating the dispersed light at angles of deviation of 40-42 degrees relative to the original path of light from the sun. These droplets actually form a circular arc, with each droplet within the arc dispersing light and reflecting it back towards the observer. Every droplet within the arc is refracting and dispersing the entire visible light spectrum

        Rainbows are not limited to the dispersion of light by raindrops. The splashing of water at the base of a waterfall caused a mist of water in the air that often results in the formation of rainbows. A backyard water sprinkler is another common source of a rainbow. Bright sunlight, suspended droplets of water and the proper angle of sighting are the three necessary components for viewing one of nature's most splendid masterpieces.

The Physics behind “Hidden Figures”

The Physics behind “Hidden Figures”

• Math plays a starring role in the movie "Hidden Figures,"
• Adapted from a book, the movie has to do with three three African-American women working as "human computers" for NASA. The film's standout math whiz is Katherine Goble Johnson.
• Johnson is shown trying to solve equations for the trajectory of astronaut John Glenn's space capsule. They're stumped until Johnson hits upon a solution: "Euler's Method,"
• How she used  Euler's Method was very helpful to sending the astronauts into orbit.
• First off, Euler's Method is indeed pretty old, if not exactly ancient. It was developed by Leonhard Euler a prolific Swiss mathematician who lived 1707-1783.
• He was a mathematician at Carnegie Mellon University
• What has come to be known as Euler's Method is just a tiny fraction of his legendary contributions.

• The method tackles what many people may not realize is a common challenge in math  often the equations just can't be solved exactly.
• When that happens, mathematicians must figure out ways to approximate the answers for specific situations.
• Euler's method is one such technique applied to what is called a differential equation. These equations often show up, among many other places, in physics problems that describe the path of a moving object subject to changing forces.
• When a capsule is flying through space, gravity is constantly tugging at it.
• How hard gravity pulls is related to distance, so as the spacecraft gets nearer to or farther away from Earth, the forces on it also change.

• One way to visualize the meaning of the equations could be as ocean currents
• As you travel through the water, the currents change direction and speed
• If you're planning to navigate from a remote island on a raft, you'd want to determine exactly how you'd float through the water, which is a pathway made up of infinitely many points which is analogous to an exact solution to a differential equation.
• Sometimes it's impossible to get an ideal solution.
• Instead, as you drift along, you could measure the current at regular time intervals.
• By knowing your starting point and assuming the current stays roughly constant between readings, you could plot an approximate trajectory.
• This process of calculating solutions at discrete points and connecting them is essentially Euler's Method
• The method works best when the points are close together and when the solution changes slowly and smoothly, because errors can accumulate at each step of the process.
• Approximating a pathway made up of infinitely many points, by linking together a finite number of calculations, is an example of something called a numerical approach in mathematics.

• Euler's Method works numerically
• Euler's Method is one of the simplest of many numerical methods that now exist for solving differential equations.
• Rudy Horne, a mathematician at Morehouse College in Atlanta, was the math advisor to the movie, and it was he who suggested Euler's Method for the key blackboard scene.
• The scene focuses on how to get John Glenn's capsule back to Earth, and Horne says NASA had derived a set of differential equations in the late 1950s to describe the re-entry.
• Euler's Method is one way to solve the equations

• The work for solving these coupled differential equations was done by the whole team of researchers at NASA and possibly in part by Katherine Johnson
• Katherine Johnson began work at the National Advisory Committee for Aeronautics, the predecessor to NASA, in 1953.
• She analyzed test flight data and helped calculate the trajectory of the first American manned space flight, Alan Shepard 1961 trip.
• In 1960, she became the first woman in the Space Flight Division to co author a published technical report.
• In the report Johnson and engineer Ted Skopinski work through some of the key calculations needed to make sure an orbiting space capsule passes over a specified latitude and longitude on the Earth.
• Such calculations were essential so that the Navy could be at the right place to rescue the astronaut once he splashed down in the ocean
• Johnson and Skopinski calculations draw upon multiple branches of math and require numerical methods.
• Complicating the picture is the fact that the Earth is not a perfect sphere, as assumed in idealized orbital mechanics calculations, but bulges slightly in the middle, like a squashed ball, which causes the capsule's orbit to shift slightly over time.
• But the full extent of the math that Katherine Johnson and the other women and men of NASA used to send astronauts safely into space and back is much richer and deeper than any one approach.

Jared Blatt

Period G

Staying Cool This Summer

We all know heat, and with summer right around the corner, the only thing most people are thinking of is having fun in the sun. But unfortunately with heat comes sweat. Sweat is the body's natural reaction to a rise in temperature. But have you ever thought about the physics of staying cool?

Sweat happens when there is an increase in the body's temperature. When temperature increases, the molecules in the substance excite. When this happens, the kinetic energy of the substance increases. So, when you cool something down, you lower its average kinetic energy.

So how does sweat cool you off? It works through the evaporation of water. Suppose we have some water at room temperature. This means that the water molecules in this group of water has an average kinetic energy of some value. But not all water molecules are the same. Instead there is a distribution of kinetic energies. Some molecules are moving quite slow and some are moving very fast. It’s possible that these very fast molecules can escape the liquid water and become gas water. What’s left is a water but now with a lower average kinetic energy since the highest KE molecules have evaporated. If this is a bead of sweat on a human, the water will be cooler than the actual skin, helping the human to cool off.

The Physics of Drones

Eliza Mahoney
Mr. Gray
Honors Physics Per. G
23 May 2017
Blog Post #7

Flying

How do drones fly? Drones use rotors for propulsion and control in their flight. A rotor can be thought of a fan, with spinning blades to push the air down. As the rotor pushes down on the air, the air pushes up on the rotor, according to Newton's third law. This is the basic idea behind the lift of the drone, which is dependent on the control of the upward and downward force. The faster the spin of the rotor, the faster the climb of the drone.

The three options a drone has in the vertical plane are to descend, hover or climb. To hover, the net force of the four rotors pushing up must be equal to the gravitational force pushing it down. This means the net force must be zero. To make the drone climb, or to increase the thrust (speed), the nonzero upward force must be greater than the weight. Otherwise known as the net force being positive. After it starts to climb, the thrust can be decreased a small amount, but now there are three forces acting on the drone: weight, thrust and air drag. So, the thrust still has to be greater than the other forces to continue the climb. Descending requires the opposite: the thrust to be decreased so it is less than the other forces, and the net force is downward, or negative. 

Turning (Rotating)

There are two sets of rotors on a drone, and with the two sets rotating in opposite directions, the angular momentum is zero. Angular momentum is very similar to linear momentum. It is calculated by multiplying the angular velocity by the moment of inertia. So, the angular momentum all depends on how fast the rotors are spinning. 

If there is no torque on the drone, then the angular momentum must remain constant. Consider one set of rotors to have a positive angular momentum and the other set to have a negative angular momentum. In a normal descent, hover, or climb, they all add up to zero. To rotate, the spin of rotors 1 and 3 must be decreased and the spin of rotors 2 and 4 must be increased. This way, the total angular momentum no longer adds up to zero but no thrust is lost and the drone remains hovering. This way, the total force remains equal to the gravitational force but the drone is rotating. Flipping the increasing of spin to rotors 1 and 3 and decreasing 2 and 4 will rotate the drone the opposite way.

Who would have thought that a drone combines many different aspects of physics in its flight? Newton's laws, torque, angular momentum, and net force are all components of keeping a drone in the air. Think about this next time you fly a drone! 

The Physics of Archery: Fake Forces

The Physics of Archery 

When you think about archery you may be very confused when watching a slowed down version of a archery such as the one below. 

 

As you can tell be able to tell just by looking at the motions of archery the force comes from the pulling back of strings as shown in the picture below.

The bow start at rest and accelerates until the bowstring stops applying force. However this does not explain why the arrow wobbles so much. This can be explained by fake forces. While fake forces may seem fake they are real. When first  understand fake forces it may seem like everything that has been taught to you in physics is a lie, because it goes against newton's second law. Newton's second law is necessary in physics but it is only applicable if  forces and accelerations are measured with respect to a constant velocity reference frame. When measures this way a fake force must be applied. The new equation is Ffake=-ma. These fake forces are not a evil new development and have probably been encountered by the average individual. This fake force is experienced while riding on an elevator. A fake force pushing down on you due to the acceleration of the elevator. This makes you feel like you have become heavier, but it is actually just  force due to a real interaction. 

Now you may be confused how this fake force causes this wobble, because not all elevators wobble. This is because there is not only a fake force acting upon this arrow in Archery.  

Now this may be confusing because it would make sense that the two forces would cancel each other out and the arrow would not move, but this is not the case. One way to picture why would happen is placing a arrow against a wall. When you place pressure on the arrow, it does not snap or stay still it bends a little. This is why during flight the arrow is constantly bending.  Once the bowstring stops applying force to the   arrow, the arrow is no longer accelerating. If the arrow is no longer accelerating, the fake force is not longer present. This results in a  bent arrow with no forces. This cause the arrow to attempt to return it’s straight shape, but it cannot stay there. When it gets to the straight position it is moving with speed. This speed  causes it to overshoot this equilibrium, and now it’s bent the other way. Thus begins the oscillating arrow, which makes it look like this is slow motion. 

Article: 

The Best Way to Crack an Egg Using Physics

The Best Way to Crack an Egg Using Physics

Paige Giffault

I'm sure everyone has cracked several, if not countless, eggs in their lives. There are those annoying and extremely time consuming occurrences when you crack the egg and accidentally drop some eggshells into the bowl. There are also time when you crack it and it just spills everywhere. Well, using a few basic physics principles, you have solved the problem of how to crack the egg perfectly.



Cracking an egg, like any object, requires a certain amount of force. Now, with something as fragile and thin as an eggshell, the amount of force used is very important. With too much force, the egg will spill everywhere, and with too little, the shell won't completely break. Positing of the applied force is also very important. According to materials scientist from Duke University, Volker Blum, "you want to initiate a crack at the flattest part of the egg, which is the middle".

The center of the egg is the weakest part of the egg. This is where you would want to break is because this is where the limit beyond which they cannot absorb more force, or its breaking point is. Unlike the top and bottom of the egg, which are the strongest part of the shell and have the most curvature, the middle is flat and therefore easier to break.

Sinan Keten, a mechanical engineer at Northwestern University compares the curvature of the top and bottom of an egg to an archway. He says that like an egg, an arch is able to hold a lot of weight without breaking because of the weight is distributed. Likewise, the shell's curves at the top and bottom are able to withstand more applied force because they can evenly distribute the pressure. 

So, now you know that in order to crack an egg perfectly, you must do it right down the middle and with the right amount of force!!